A crew of violent thugs used a sickening ploy to rob a Long Island home — they posed as volunteers passing out brochures on President Obama’s health-care plan, authorities said yesterday.

Suffolk County prosecutors claim Benjamin Thompson, 31, of Brooklyn, had a stethoscope around his neck while Natalie Desir, 26 of Nyack, held a clipboard when they approached a Huntington home on Aug. 29 claiming to have pamphlets on Obama’s proposals to reform the health-insurance industry.

They allegedly said they could help people claim a $500 credit.

But as soon as a woman living at the home opened the door, the duo pushed their way in at gunpoint with the help of an accomplice, Vance Jackson, 46, of Yonkers, who had been hiding outside, the DA said.

They allegedly shot one male resident four times and shot the woman in her foot. They then pistol-whipped the woman’s mother before fleeing with $4,000 in cash with the help of alleged getaway driver Theodore Briffs, 40, of The Bronx, prosecutors said.